Should the law restrict what animals can be kept as pets?

I can see that having to get a permit to keep an exotic animal would be a good thing, and I certainly think that this should also include all of the constrictor snakes that people keep. It was only a few months ago that two children were killed by an escaped large snake. Any animal that can be considered dangerous if it escapes should be licensed and regulated. Any kind of large cat, lion, tiger, even a bobcat or lynx, should all either not be legal, or be strictly regulated to be sure that they can't escape and maul or kill someone.
Otherwise, I am basically against the government conntrolling all aspects of people's lives, and I do not want to see any unnecessary laws passed for people to have to live with. If someone is abusing an animal, or even neglecting it; there are already laws against that, and those would cover both the usual pets like cats and dogs, as well as the more exotic pets.